/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2006

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 /// \ingroup graph_concepts

 /// \file

 /// \brief Undirected bipartite graphs and components of.

 #ifndef LEMON_CONCEPT_BPUGRAPH_H

 #define LEMON_CONCEPT_BPUGRAPH_H

 #include <lemon/concept/graph_components.h>

 #include <lemon/concept/graph.h>

 #include <lemon/concept/ugraph.h>

 #include <lemon/bits/utility.h>

 namespace lemon {

   namespace concept {

     /// \addtogroup graph_concepts

     /// @{

     /// \brief Class describing the concept of Bipartite Undirected Graphs.

     ///

     /// This class describes the common interface of all 

     /// Undirected Bipartite Graphs.

     ///

     /// As all concept describing classes it provides only interface

     /// without any sensible implementation. So any algorithm for

     /// bipartite undirected graph should compile with this class, but it 

     /// will not run properly, of course.

     ///

     /// In LEMON bipartite undirected graphs also fulfill the concept of 

     /// the undirected graphs (\ref lemon::concept::UGraph "UGraph Concept"). 

     ///

     /// You can assume that all undirected bipartite graph can be handled

     /// as an undirected graph and consequently as a static graph.

     ///

     /// The bipartite graph stores two types of nodes which are named

     /// ANode and BNode. The graph type contains two types ANode and

     /// BNode which are inherited from Node type. Moreover they have

     /// constructor which converts Node to either ANode or BNode when

     /// it is possible. Therefor everywhere the Node type can be used

     /// instead of ANode and BNode. So the usage of the ANode and

     /// BNode is not suggested.

     ///

     /// The iteration on the partition can be done with the ANodeIt and 

     /// BNodeIt classes. The node map can be used to map values to the nodes

     /// and similarly we can use to map values for just the ANodes and

     /// BNodes the ANodeMap and BNodeMap template classes.

     class BpUGraph {

     public:

       /// \brief The undirected graph should be tagged by the

       /// UndirectedTag.

       ///

       /// The undirected graph should be tagged by the UndirectedTag. This

       /// tag helps the enable_if technics to make compile time 

       /// specializations for undirected graphs.  

       typedef True UndirectedTag;

       /// \brief The base type of node iterators, 

       /// or in other words, the trivial node iterator.

       ///

       /// This is the base type of each node iterator,

       /// thus each kind of node iterator converts to this.

       /// More precisely each kind of node iterator should be inherited 

       /// from the trivial node iterator. The Node class represents

       /// both of two types of nodes. 

       class Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Node() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Node(const Node&) { }

         /// Invalid constructor \& conversion.

         /// This constructor initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         Node(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(Node) const { return true; }

         /// Inequality operator

         /// \sa operator==(Node n)

         ///

         bool operator!=(Node) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	bool operator<(Node) const { return false; }

       };

       /// \brief Helper class for ANodes.

       ///

       /// This class is just a helper class for ANodes, it is not

       /// suggested to use it directly. It can be converted easily to

       /// node and vice versa. The usage of this class is limited

       /// two use just as template parameters for special map types. 

       class ANode {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         ANode() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         ANode(const ANode&) { }

         /// Construct the same node as ANode.

         /// Construct the same node as ANode. It may throws assertion

         /// when the given node is from the BNode set.

         ANode(const Node&) { }

         /// Invalid constructor \& conversion.

         /// This constructor initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         ANode(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(ANode) const { return true; }

         /// Inequality operator

         /// \sa operator==(ANode n)

         ///

         bool operator!=(ANode) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	bool operator<(ANode) const { return false; }

       };

       /// \brief Helper class for BNodes.

       ///

       /// This class is just a helper class for BNodes, it is not

       /// suggested to use it directly. It can be converted easily to

       /// node and vice versa. The usage of this class is limited

       /// two use just as template parameters for special map types. 

       class BNode {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         BNode() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         BNode(const BNode&) { }

         /// Construct the same node as BNode.

         /// Construct the same node as BNode. It may throws assertion

         /// when the given node is from the ANode set.

         BNode(const Node&) { }

         /// Invalid constructor \& conversion.

         /// This constructor initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         BNode(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(BNode) const { return true; }

         /// Inequality operator

         /// \sa operator==(BNode n)

         ///

         bool operator!=(BNode) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	bool operator<(BNode) const { return false; }

       };

       /// This iterator goes through each node.

       /// This iterator goes through each node.

       /// Its usage is quite simple, for example you can count the number

       /// of nodes in graph \c g of type \c Graph like this:

       ///\code

       /// int count=0;

       /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;

       ///\endcode

       class NodeIt : public Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         NodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         NodeIt(const NodeIt& n) : Node(n) { }

         /// Invalid constructor \& conversion.

         /// Initialize the iterator to be invalid.

         /// \sa Invalid for more details.

         NodeIt(Invalid) { }

         /// Sets the iterator to the first node.

         /// Sets the iterator to the first node of \c g.

         ///

         NodeIt(const BpUGraph&) { }

         /// Node -> NodeIt conversion.

         /// Sets the iterator to the node of \c the graph pointed by 

 	/// the trivial iterator.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         NodeIt(const BpUGraph&, const Node&) { }

         /// Next node.

         /// Assign the iterator to the next node.

         ///

         NodeIt& operator++() { return *this; }

       };

       /// This iterator goes through each ANode.

       /// This iterator goes through each ANode.

       /// Its usage is quite simple, for example you can count the number

       /// of nodes in graph \c g of type \c Graph like this:

       ///\code

       /// int count=0;

       /// for (Graph::ANodeIt n(g); n!=INVALID; ++n) ++count;

       ///\endcode

       class ANodeIt : public Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         ANodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         ANodeIt(const ANodeIt& n) : Node(n) { }

         /// Invalid constructor \& conversion.

         /// Initialize the iterator to be invalid.

         /// \sa Invalid for more details.

         ANodeIt(Invalid) { }

         /// Sets the iterator to the first node.

         /// Sets the iterator to the first node of \c g.

         ///

         ANodeIt(const BpUGraph&) { }

         /// Node -> ANodeIt conversion.

         /// Sets the iterator to the node of \c the graph pointed by 

 	/// the trivial iterator.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         ANodeIt(const BpUGraph&, const Node&) { }

         /// Next node.

         /// Assign the iterator to the next node.

         ///

         ANodeIt& operator++() { return *this; }

       };

       /// This iterator goes through each BNode.

       /// This iterator goes through each BNode.

       /// Its usage is quite simple, for example you can count the number

       /// of nodes in graph \c g of type \c Graph like this:

       ///\code

       /// int count=0;

       /// for (Graph::BNodeIt n(g); n!=INVALID; ++n) ++count;

       ///\endcode

       class BNodeIt : public Node {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         BNodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         BNodeIt(const BNodeIt& n) : Node(n) { }

         /// Invalid constructor \& conversion.

         /// Initialize the iterator to be invalid.

         /// \sa Invalid for more details.

         BNodeIt(Invalid) { }

         /// Sets the iterator to the first node.

         /// Sets the iterator to the first node of \c g.

         ///

         BNodeIt(const BpUGraph&) { }

         /// Node -> BNodeIt conversion.

         /// Sets the iterator to the node of \c the graph pointed by 

 	/// the trivial iterator.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         BNodeIt(const BpUGraph&, const Node&) { }

         /// Next node.

         /// Assign the iterator to the next node.

         ///

         BNodeIt& operator++() { return *this; }

       };

       /// The base type of the undirected edge iterators.

       /// The base type of the undirected edge iterators.

       ///

       class UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         UEdge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         UEdge(const UEdge&) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         UEdge(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(UEdge) const { return true; }

         /// Inequality operator

         /// \sa operator==(UEdge n)

         ///

         bool operator!=(UEdge) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	bool operator<(UEdge) const { return false; }

       };

       /// This iterator goes through each undirected edge.

       /// This iterator goes through each undirected edge of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of undirected edges in a graph \c g of type \c Graph as follows:

       ///\code

       /// int count=0;

       /// for(Graph::UEdgeIt e(g); e!=INVALID; ++e) ++count;

       ///\endcode

       class UEdgeIt : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         UEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         UEdgeIt(const UEdgeIt& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         UEdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first undirected edge.

         /// This constructor sets the iterator to the first undirected edge.

         UEdgeIt(const BpUGraph&) { }

         /// UEdge -> UEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator.

         /// This feature necessitates that each time we

         /// iterate the undirected edge-set, the iteration order is the 

 	/// same.

         UEdgeIt(const BpUGraph&, const UEdge&) { } 

         /// Next undirected edge

         /// Assign the iterator to the next undirected edge.

         UEdgeIt& operator++() { return *this; }

       };

       /// \brief This iterator goes trough the incident undirected 

       /// edges of a node.

       ///

       /// This iterator goes trough the incident undirected edges

       /// of a certain node

       /// of a graph.

       /// Its usage is quite simple, for example you can compute the

       /// degree (i.e. count the number

       /// of incident edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       ///\code

       /// int count=0;

       /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       ///\endcode

       class IncEdgeIt : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         IncEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         IncEdgeIt(const IncEdgeIt& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         IncEdgeIt(Invalid) { }

         /// This constructor sets the iterator to first incident edge.

         /// This constructor set the iterator to the first incident edge of

         /// the node.

         IncEdgeIt(const BpUGraph&, const Node&) { }

         /// UEdge -> IncEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         IncEdgeIt(const BpUGraph&, const UEdge&) { }

         /// Next incident edge

         /// Assign the iterator to the next incident edge

 	/// of the corresponding node.

         IncEdgeIt& operator++() { return *this; }

       };

       /// The directed edge type.

       /// The directed edge type. It can be converted to the

       /// undirected edge.

       class Edge : public UEdge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Edge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Edge(const Edge& e) : UEdge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         Edge(Invalid) { }

         /// Equality operator

         /// Two iterators are equal if and only if they point to the

         /// same object or both are invalid.

         bool operator==(Edge) const { return true; }

         /// Inequality operator

         /// \sa operator==(Edge n)

         ///

         bool operator!=(Edge) const { return true; }

 	/// Artificial ordering operator.

 	/// To allow the use of graph descriptors as key type in std::map or

 	/// similar associative container we require this.

 	///

 	/// \note This operator only have to define some strict ordering of

 	/// the items; this order has nothing to do with the iteration

 	/// ordering of the items.

 	bool operator<(Edge) const { return false; }

       }; 

       /// This iterator goes through each directed edge.

       /// This iterator goes through each edge of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of edges in a graph \c g of type \c Graph as follows:

       ///\code

       /// int count=0;

       /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;

       ///\endcode

       class EdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         EdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         EdgeIt(const EdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         EdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first edge.

         /// This constructor sets the iterator to the first edge of \c g.

         ///@param g the graph

         EdgeIt(const BpUGraph &g) { ignore_unused_variable_warning(g); }

         /// Edge -> EdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         EdgeIt(const BpUGraph&, const Edge&) { } 

         ///Next edge

         /// Assign the iterator to the next edge.

         EdgeIt& operator++() { return *this; }

       };

       /// This iterator goes trough the outgoing directed edges of a node.

       /// This iterator goes trough the \e outgoing edges of a certain node

       /// of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of outgoing edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       ///\code

       /// int count=0;

       /// for (Graph::OutEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       ///\endcode

       class OutEdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         OutEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         OutEdgeIt(const OutEdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         OutEdgeIt(Invalid) { }

         /// This constructor sets the iterator to the first outgoing edge.

         /// This constructor sets the iterator to the first outgoing edge of

         /// the node.

         ///@param n the node

         ///@param g the graph

         OutEdgeIt(const BpUGraph& n, const Node& g) {

 	  ignore_unused_variable_warning(n);

 	  ignore_unused_variable_warning(g);

 	}

         /// Edge -> OutEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator.

 	/// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         OutEdgeIt(const BpUGraph&, const Edge&) { }

         ///Next outgoing edge

         /// Assign the iterator to the next 

         /// outgoing edge of the corresponding node.

         OutEdgeIt& operator++() { return *this; }

       };

       /// This iterator goes trough the incoming directed edges of a node.

       /// This iterator goes trough the \e incoming edges of a certain node

       /// of a graph.

       /// Its usage is quite simple, for example you can count the number

       /// of outgoing edges of a node \c n

       /// in graph \c g of type \c Graph as follows.

       ///\code

       /// int count=0;

       /// for(Graph::InEdgeIt e(g, n); e!=INVALID; ++e) ++count;

       ///\endcode

       class InEdgeIt : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         InEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         InEdgeIt(const InEdgeIt& e) : Edge(e) { }

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         InEdgeIt(Invalid) { }

         /// This constructor sets the iterator to first incoming edge.

         /// This constructor set the iterator to the first incoming edge of

         /// the node.

         ///@param n the node

         ///@param g the graph

         InEdgeIt(const BpUGraph& g, const Node& n) { 

 	  ignore_unused_variable_warning(n);

 	  ignore_unused_variable_warning(g);

 	}

         /// Edge -> InEdgeIt conversion

         /// Sets the iterator to the value of the trivial iterator \c e.

         /// This feature necessitates that each time we 

         /// iterate the edge-set, the iteration order is the same.

         InEdgeIt(const BpUGraph&, const Edge&) { }

         /// Next incoming edge

         /// Assign the iterator to the next inedge of the corresponding node.

         ///

         InEdgeIt& operator++() { return *this; }

       };

       /// \brief Read write map of the nodes to type \c T.

       /// 

       /// ReadWrite map of the nodes to type \c T.

       /// \sa Reference

       /// \warning Making maps that can handle bool type (NodeMap<bool>)

       /// needs some extra attention!

       /// \todo Wrong documentation

       template<class T> 

       class NodeMap : public ReadWriteMap< Node, T >

       {

       public:

         ///\e

         NodeMap(const BpUGraph&) { }

         ///\e

         NodeMap(const BpUGraph&, T) { }

         ///Copy constructor

         NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

         ///Assignment operator

         NodeMap& operator=(const NodeMap&) { return *this; }

         // \todo fix this concept

       };

       /// \brief Read write map of the ANodes to type \c T.

       /// 

       /// ReadWrite map of the ANodes to type \c T.

       /// \sa Reference

       /// \warning Making maps that can handle bool type (NodeMap<bool>)

       /// needs some extra attention!

       /// \todo Wrong documentation

       template<class T> 

       class ANodeMap : public ReadWriteMap< Node, T >

       {

       public:

         ///\e

         ANodeMap(const BpUGraph&) { }

         ///\e

         ANodeMap(const BpUGraph&, T) { }

         ///Copy constructor

         ANodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

         ///Assignment operator

         ANodeMap& operator=(const NodeMap&) { return *this; }

         // \todo fix this concept

       };

       /// \brief Read write map of the BNodes to type \c T.

       /// 

       /// ReadWrite map of the BNodes to type \c T.

       /// \sa Reference

       /// \warning Making maps that can handle bool type (NodeMap<bool>)

       /// needs some extra attention!

       /// \todo Wrong documentation

       template<class T> 

       class BNodeMap : public ReadWriteMap< Node, T >

       {

       public:

         ///\e

         BNodeMap(const BpUGraph&) { }

         ///\e

         BNodeMap(const BpUGraph&, T) { }

         ///Copy constructor

         BNodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

         ///Assignment operator

         BNodeMap& operator=(const NodeMap&) { return *this; }

         // \todo fix this concept

       };

       /// \brief Read write map of the directed edges to type \c T.

       ///

       /// Reference map of the directed edges to type \c T.

       /// \sa Reference

       /// \warning Making maps that can handle bool type (EdgeMap<bool>)

       /// needs some extra attention!

       /// \todo Wrong documentation

       template<class T> 

       class EdgeMap : public ReadWriteMap<Edge,T>

       {

       public:

         ///\e

         EdgeMap(const BpUGraph&) { }

         ///\e

         EdgeMap(const BpUGraph&, T) { }

         ///Copy constructor

         EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) { }

         ///Assignment operator

         EdgeMap& operator=(const EdgeMap&) { return *this; }

         // \todo fix this concept    

       };

       /// Read write map of the undirected edges to type \c T.

       /// Reference map of the edges to type \c T.

       /// \sa Reference

       /// \warning Making maps that can handle bool type (UEdgeMap<bool>)

       /// needs some extra attention!

       /// \todo Wrong documentation

       template<class T> 

       class UEdgeMap : public ReadWriteMap<UEdge,T>

       {

       public:

         ///\e

         UEdgeMap(const BpUGraph&) { }

         ///\e

         UEdgeMap(const BpUGraph&, T) { }

         ///Copy constructor

         UEdgeMap(const UEdgeMap& em) : ReadWriteMap<UEdge,T>(em) {}

         ///Assignment operator

         UEdgeMap &operator=(const UEdgeMap&) { return *this; }

         // \todo fix this concept    

       };

       /// \brief Direct the given undirected edge.

       ///

       /// Direct the given undirected edge. The returned edge source

       /// will be the given node.

       Edge direct(const UEdge&, const Node&) const {

 	return INVALID;

       }

       /// \brief Direct the given undirected edge.

       ///

       /// Direct the given undirected edge. The returned edge

       /// represents the given undireted edge and the direction comes

       /// from the given bool.  The source of the undirected edge and

       /// the directed edge is the same when the given bool is true.

       Edge direct(const UEdge&, bool) const {

 	return INVALID;

       }

       /// \brief Returns true when the given node is an ANode.

       ///

       /// Returns true when the given node is an ANode.

       bool aNode(Node) const { return true;}

       /// \brief Returns true when the given node is an BNode.

       ///

       /// Returns true when the given node is an BNode.

       bool bNode(Node) const { return true;}

       /// \brief Returns the edge's end node which is in the ANode set.

       ///

       /// Returns the edge's end node which is in the ANode set.

       Node aNode(UEdge) const { return INVALID;}

       /// \brief Returns the edge's end node which is in the BNode set.

       ///

       /// Returns the edge's end node which is in the BNode set.

       Node bNode(UEdge) const { return INVALID;}

       /// \brief Returns true if the edge has default orientation.

       ///

       /// Returns whether the given directed edge is same orientation as

       /// the corresponding undirected edge's default orientation.

       bool direction(Edge) const { return true; }

       /// \brief Returns the opposite directed edge.

       ///

       /// Returns the opposite directed edge.

       Edge oppositeEdge(Edge) const { return INVALID; }

       /// \brief Opposite node on an edge

       ///

       /// \return the opposite of the given Node on the given UEdge

       Node oppositeNode(Node, UEdge) const { return INVALID; }

       /// \brief First node of the undirected edge.

       ///

       /// \return the first node of the given UEdge.

       ///

       /// Naturally undirected edges don't have direction and thus

       /// don't have source and target node. But we use these two methods

       /// to query the two endnodes of the edge. The direction of the edge

       /// which arises this way is called the inherent direction of the

       /// undirected edge, and is used to define the "default" direction

       /// of the directed versions of the edges.

       /// \sa direction

       Node source(UEdge) const { return INVALID; }

       /// \brief Second node of the undirected edge.

       Node target(UEdge) const { return INVALID; }

       /// \brief Source node of the directed edge.

       Node source(Edge) const { return INVALID; }

       /// \brief Target node of the directed edge.

       Node target(Edge) const { return INVALID; }

       /// \brief Base node of the iterator

       ///

       /// Returns the base node (the source in this case) of the iterator

       Node baseNode(OutEdgeIt e) const {

 	return source(e);

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node (the target in this case) of the

       /// iterator

       Node runningNode(OutEdgeIt e) const {

 	return target(e);

       }

       /// \brief Base node of the iterator

       ///

       /// Returns the base node (the target in this case) of the iterator

       Node baseNode(InEdgeIt e) const {

 	return target(e);

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node (the source in this case) of the

       /// iterator

       Node runningNode(InEdgeIt e) const {

 	return source(e);

       }

       /// \brief Base node of the iterator

       ///

       /// Returns the base node of the iterator

       Node baseNode(IncEdgeIt) const {

 	return INVALID;

       }

       /// \brief Running node of the iterator

       ///

       /// Returns the running node of the iterator

       Node runningNode(IncEdgeIt) const {

 	return INVALID;

       }

       template <typename Graph>

       struct Constraints {

 	void constraints() {

 	}

       };

     };

     /// @}

   }

 }

 #endif